Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
466 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#16837214 | C2 | semidirect |
| 3. #21425831 | C2 | semidirect |
| 4. #21425823 | C2 | semidirect |
| 5. #21425811 | C2 | semidirect |
| 6. #21425701 | C2 | semidirect |
| 7. C59×#1833 | C2 | semidirect |
| 15. #16837786 | C4 | semidirect |
| 16. #16837779 | C4 | semidirect |
| 53. #14273667 | D4 | semidirect |
| 55. C2×C59⋊C16 | D4 | semidirect |
| 175. #1833 | D59 | semidirect |
| 201. C59 | #13215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434582 | 2 |
| C2×#16837214 | 2 |
| #21425831 | 2 |
| #21425823 | 2 |
| #21425811 | 2 |
| #21425701 | 2 |
| C59×#1833 | 2 |
| #13215 | 59 |